trigonometry - Multiply complex numbers to show trigonometric addition formulas

Use the rules for multiplication of two complex numbers written in the form $r(\cos\theta +i\sin\theta)$ to show that $\sin(\theta_1 +\theta_2)=\sin\theta_1\cos\theta_2 +\sin\theta_2\cos\theta_1$ and $\cos(\theta_1 +\theta_2)=\cos\theta_1\cos\theta_2 −\sin\theta_1\sin\theta_2$.

I have no idea how to do this. It's part of a complex number worksheet but I can't find a way to do it. I thought about using Euler's formula but got no where. Thank you in advance